So as I understand it database hardening is a process in which you remove the vulnerabilities that result from lax con-figuration options. This can sometimes compensate for exploitable vendor bugs.

Three main stages exist in hardening a database:

Locking down access to resources that can be misused.

Disabling functions that are not required.

Principle of least authority or least privileges.

There is a wealth of information for "locking down" RDBMS environments to harden them against attacks. However these resources don’t provide enough context on current exploitations for databases (if you don’t know what types of attacks exist and which ones are popular, how do you know if your hardening measures are going to provide protection).

A bad way for me to begin learning hardening techniques would be to list as many database exploitations out there and learning how each and every one of them work, that could take... a very long time.

So I am wondering where I can begin, resources available and current trends etc.

Added a repose below, but in general, attacks are either in the underlying code of the DBMS, which would be a patching issue or will be in certain type of vector which is addressed through hardening and general controls. E.g., permissions on tables/views, good passwords, SQL injection, memory management. It is not very often there is a new "class" of attack per-se.
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Eric GFeb 21 '13 at 5:06

From your post, it is not clear if you are working in a web environment, but you probably want to know about SQL injection, etc. I'd start at OWASP. They have some general information on SQL injection, some secure guidelines, and some testing guidelines.